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Solve using the zero product property.
a. (v – 5)(v – 9) = 0
b. (z + 3)(z – 2) = 0
c. (m + 1)(m – 3) = 0
d. (h – 2)(h – 1) = 0
e. (w + 1)(w + 2) = 0
f. (q – 2)(q + 1) = 0
g. (k – 1)(k – 5) = 0
h. (r + 3)(r + 2) = 0
i.
(a + 6)(a – 7) = 0
j.
(y – 4)(y + 1) = 0
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WORKSHEET – SOLVE A QUADRATIC EQUATION USING
THE ZERO PRODUCT PROPERTY www.emathematics.net
KEYS
a. (v – 5)(v – 9) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (v – 5)(v – 9) = 0, then
(v – 5) must be 0 or (v – 9) must be 0.
Write two equations and solve for v.
v–5=0
or
v=5
v–9=0
v=9
The solution is v = 5 or v = 9
b. (z + 3)(z – 2) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (z + 3)(z – 2) = 0, then
(z + 3) must be 0 or (z – 2) must be 0.
Write two equations and solve for z.
z+3=0
or
z–2= 0
z = -3
z=2
The solution is z = -3 or z = 2
c. (m + 1)(m – 3) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
2
WORKSHEET – SOLVE A QUADRATIC EQUATION USING
THE ZERO PRODUCT PROPERTY www.emathematics.net
According to the Zero Product Property, if (m + 1)(m – 3) = 0, then
(m + 1) must be 0 or (m – 3) must be 0.
Write two equations and solve for m.
m+1=0
or
m–3= 0
m = -1
m=3
The solution is m = -1 or m = 3
d. (h – 2)(h – 1) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (h – 2)(h – 1) = 0, then
(h – 2) must be 0 or (h – 1) must be 0.
Write two equations and solve for h.
h–2=0
or
h=2
h–1=0
h=1
The solution is h = 2 or h = 1
e. (w + 1)(w + 2) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (w + 1)(w + 2) = 0, then
(w + 1) must be 0 or (w + 2) must be 0.
Write two equations and solve for w.
w+1=0
or
w+2=0
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WORKSHEET – SOLVE A QUADRATIC EQUATION USING
THE ZERO PRODUCT PROPERTY www.emathematics.net
w = -1
w = -2
The solution is w = -1 or w = -2
f. (q – 2)(q + 1) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (q – 2)(q + 1) = 0, then
(q – 2) must be 0 or (q + 1) must be 0.
Write two equations and solve for q.
q–2=0
or
q=2
q+1=0
q = -1
The solution is q = 2 or q = -1
g. (k – 1)(k – 5) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (k – 1)(k – 5) = 0, then
(k – 1) must be 0 or (k – 5) must be 0.
Write two equations and solve for k.
k–1=0
or
k =1
k–5=0
k=5
The solution is k = 1 or k = 5
h. (r + 3)(w + 2) = 0
The Zero Product Property states that for all real numbers a and b:
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WORKSHEET – SOLVE A QUADRATIC EQUATION USING
THE ZERO PRODUCT PROPERTY www.emathematics.net
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (r + 3)(r + 2) = 0, then
(r + 3) must be 0 or (r + 2) must be 0.
Write two equations and solve for r.
r+3=0
or
r+2=0
r = -3
r = -2
The solution is r = -3 or r = -2
i.
(a + 6)(a – 7) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (a + 6)(a – 7) = 0, then
(a + 6) must be 0 or (a – 7) must be 0.
Write two equations and solve for a.
a+6=0
or
a–7= 0
a = -6
a=7
The solution is a = -6 or a = 7
j.
(y – 4)(y + 1) = 0
The Zero Product Property states that for all real numbers a and b:
If ab = 0, then a = 0 or b = 0
According to the Zero Product Property, if (y – 4)(y + 1) = 0, then
(y – 4) must be 0 or (y + 1) must be 0.
Write two equations and solve for y.
5
WORKSHEET – SOLVE A QUADRATIC EQUATION USING
THE ZERO PRODUCT PROPERTY www.emathematics.net
y–4=0
y=4
or
y+1=0
y = -1
The solution is y = 4 or y = -1
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